FIBONACCI NUMBERS. C haitanya khurana Class 9 th Roll No ---08 Bhaskar House Step By Step School, Noida. Definition. The Fibonacci numbers can be rather simply defined by the following: 1. Start with the numbers 1 and
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Roll No ---08
Step By Step School, Noida
The Fibonacci numbers can be rather simply
defined by the following:
More formally: [F1=1; F2=2], [F3=3], [Fn=Fn-1+Fn-2]. The resulting sequence begins like this:
F(0)=0, F(1)=1, F(n)=F(n-1)+F(n-2) for n>1.
Fn Number Fn Number Fn Number Fn Number
F0 0 F13 233 F30 832040 F39 63245986
F1 1 F14 377 F27 196418 F40 102334155
F2 1 F15 610 F28 317811
F3 2 F16 987 F29 514229
F4 3 F17 1597 F30 832040
F5 5 F18 2584 F31 1346269
F6 8 F19 4181 F32 2178309
F7 13 F20 6765 F33 3524578
F8 21 F21 10946 F34 5702887
F9 34 F22 17711 F35 9227465
F10 55 F23 28657 F36 14930352
F11 89 F24 46368 F37 24157817
F12 144 F25 75025 F38 39088169
Leonardo Fibonacci was born around 1170 to GuglielmoBonacci, a wealthy Italian merchant. Guglielmo directed a trading post (by some accounts he was the consultant for Pisa) in Bugia, a port east of Algiers in the Almohaddynasty’s sultanate in North Africa(now Bejaia, Algeria). As a young boy, Leonardo traveled with him to help; it was there he learned about the Hindu–Arabic numeral system.
The Fibonacci numbers are Nature's numbering system. They appear everywhere in Nature, from the leaf arrangement in plants, to the pattern of the florets of a flower, the bracts of a pinecone, or the scales of a pineapple. The Fibonacci numbers are therefore applicable to the growth of every living thing, including a single cell, a grain of wheat, a hive of bees, and even all of mankind.
In the case of tapered pinecones or pineapples, we see a double set of spirals – one going in a clockwise direction and one in the opposite direction. When these spirals are counted, the two sets are found to be adjacent Fibonacci numbers.
As well, many flowers have a Fibonacci number of petals. Some, like this rose, also have Fibonacci Spiral, petal arrangements.
Branching plants also exhibit Fibonacci numbers. Again, this design provides the best physical accommodation for the number of branches, while maximizing sun exposure